{"@context":"https://schema.org/","@type":"Quiz","name":"

Which of the following is equivalent to the sum of $3x^{4}+2x^{3}$ and $4x^{4}+7x^{3}$?

","hasPart":{"@type":"Question","typicalAgeRange":"12-22","educationalAlignment":[{"@type":"AlignmentObject","alignmentType":"educationalSubject","targetName":"SAT"},{"@type":"AlignmentObject","alignmentType":"educationalLevel","targetName":"SAT","educationalFramework":"Common Core","targetUrl":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-157"}],"about":{"@type":"Thing","name":"Math, Advanced Math, Duplicate"},"educationalLevel":"intermediate","eduQuestionType":"Multiple choice","learningResourceType":"Practice problem","assesses":["Math","Advanced Math","Duplicate"],"name":"

Which of the following is equivalent to the sum of $3x^{4}+2x^{3}$ and $4x^{4}+7x^{3}$?

","comment":{"@type":"Comment","text":"

Choice D is correct. Adding the two expressions yields $3x^{4}+2x^{3}+4x^{4}+7x^{3}$. Because the pair of terms $3x^{4}$ and $4x^{4}$ and the pair of terms $2x^{3}$ and $7x^{3}$ each contain the same variable raised to the same power, they are like terms and can be combined as $7x^{4}$ and $9x^{3}$, respectively. The sum of the given expressions therefore simplifies to $7x^{4}+9x^{3}$.

Choice A is incorrect and may result from adding the coefficients and the exponents in the given expressions. Choice B is incorrect and may result from adding the exponents as well as the coefficients of the like terms in the given expressions. Choice C is incorrect and may result from multiplying, rather than adding, the coefficients of the like terms in the given expressions.

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Which of the following is equivalent to the sum of $3x^{4}+2x^{3}$ and $4x^{4}+7x^{3}$?

","suggestedAnswer":[{"@type":"Answer","position":0,"encodingFormat":"text/html","text":"

$16x^{14}$

"},{"@type":"Answer","position":1,"encodingFormat":"text/html","text":"

$7x^{8}+9x^{6}$

"},{"@type":"Answer","position":2,"encodingFormat":"text/html","text":"

$12x^{4}+14x^{3}$

"}],"acceptedAnswer":{"@type":"Answer","position":3,"encodingFormat":"text/html","text":"

$7x^{4}+9x^{3}$

","comment":{"@type":"Comment","text":"

"},"answerExplanation":{"@type":"Comment","text":"

"}}},"url":"https://classnotes.xyz/mcqs/sat-math-advanced-math-multiple-choice-question-157"}